How do you break up with a co-worker whom you see everyday?

Unfortunately this is not going to be easy. The best thing you could do is be upfront, honest, polite, and empathetic. Make it clear that you would like to keep things civil around work and to keep your personal lives just that personal. I realize it is hard to find the words but always treat people the way you would like to be treated and although it may be awkward at work at first things will relax after time goes by. Keep your distance but don't avoid and if you run into one another keep it friendly but of course not too friendly - civil friendly.